Q24. - Algebra 2

Question

Graph each inequality.

$y\ge \frac{1}{2}x-5$.

Step-by-Step Solution

Answer

The graph of the inequality is shown below:

Step 1 – Find the boundary line equation of the given equation.

Consider the inequality $y\ge \frac{1}{2}x-5$.

The boundary line equaton is $y=\frac{1}{2}x-5$.

Here the inequality is $\ge$, graph the boundary line as a solid line.

The slope intercept form is $y=\frac{1}{2}x-5$ with slope $\frac{1}{2}.$

Step 2 – Choose a test point and test the inequality.

Choose the test point as $\left(0,0\right).$

Substitute $x=0,y=0$ in $y\ge \frac{1}{2}x-5$:

$\begin{array}{l}y\ge \frac{1}{2}x-5\\ 0\ge \frac{1}{2}\left(0\right)-5\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}substitute 0 for }x,0\text{ for }y\\ 0\ge -5\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}true}\end{array}$

Step 3 – Conclusion

Since, $0\ge -5$results a true inequality, so, shade the region that contains the point $\left(0,0\right).$

Graphical representation of $y\ge \frac{1}{2}x-5$: